Group actions, non-Kähler complex manifolds and SKT structures

Group actions, non-Kähler complex manifolds and SKT structures AbstractWe give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler) complex structures on tangential frame bundles of complex orbifolds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Complex Manifolds de Gruyter

Group actions, non-Kähler complex manifolds and SKT structures

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Publisher
de Gruyter
Copyright
© 2018 Mainak Poddar, Ajay Singh Thakur, published by De Gruyter
ISSN
2300-7443
eISSN
2300-7443
D.O.I.
10.1515/coma-2018-0002
Publisher site
See Article on Publisher Site

Abstract

AbstractWe give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler) complex structures on tangential frame bundles of complex orbifolds.

Journal

Complex Manifoldsde Gruyter

Published: Feb 2, 2018

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